Heat olive oil in a large pot and add onions, carrots, celery, and bell pepper with salt. Cover and cook on low for 15 minutes.
Add thyme, diced potatoes, and vegetable stock, then simmer until the potatoes are soft, about 10 minutes. Add beer.
In a separate pot, heat milk until it just boils. Toss cheese with flour in a bowl, then add to the hot milk and stir until melted and thickened.
Combine the cheese mixture with the vegetable pot, adding mustard, Worcestershire sauce, hot sauce, and salt and pepper to taste. Stir frequently and simmer for at least 10 minutes.
Taste and adjust seasoning before serving with bread.